Huge crowds gathered in Mexico on Sunday to condemn government moves to shrink the electoral authority as a threat to democracy, in what appeared to be the largest protest so far against President Andres Manuel Lopez Obrador's administration.

Organisers said over 500,000 people turned out in Mexico City, with video footage on social media showing the central Zocalo square filled with protesters, who also spilled out into adjoining streets. One police officer nearby said he had heard the half-a-million figure, while others gave lower estimates.

Mexico's Congress on Wednesday approved a major overhaul of the National Electoral Institute (INE), an independent body which Lopez Obrador has attacked as corrupt and inefficient.

The 69-year-old president denies his changes will weaken Mexican democracy. Critics have vowed to take the legislation, which slashes the INE's budget and staff as well as paring back its responsibilities, to the Supreme Court.

Veronica Echevarria, a 58-year-old psychologist from Mexico City at the protest, said she feared Lopez Obrador's INE shake-up was a bid by the president to stay in power. He denies this.

"We're fighting to defend our democracy," Echevarria said, wearing a cap emblazoned with the words "Hands off the INE."

She and thousands of others converged on the Zocalo on Sunday morning, many of them holding Mexican flags and dressed in pink, the INE's colour. Shouts of "Viva Mexico!" and "Lopez out!" rang out periodically as the mass of people advanced.

The Zocalo has over the years hosted many rallies fronted by Lopez Obrador, both as president and during his long career as an opposition scourge of the Mexican establishment.

The INE and its predecessor played a key role in creating a pluralistic democracy that in 2000 ended decades of one-party rule, according to many political analysts.

Fernando Belaunzaran, an opposition politician who helped to organise the protests, argued the INE changes weakened the electoral system and increased the risk of disputes clouding the 2024 elections when Lopez Obrador's successor will be chosen.

"Normally presidents try to have governability and stability for their succession, but this president is creating uncertainty," said Belaunzaran. "He's playing with fire."

Mexican presidents may only serve a single six-year term.

Belaunzaran said on Twitter that more than 500,000 people had gathered in the capital on Sunday to oppose the INE overhaul. He said demonstrations were taking place in more than 100 cities.

Protests were held in states including Jalisco, Yucatan, Nuevo Leon, Queretaro, Guanajuato and Veracruz, according to news reports and footage broadcast on social media.

At least 22,000 people gathered in Nuevo Leon's capital Monterrey, newspaper Excelsior said, citing local authorities. Another 20,000 took to the streets in the heart of the Jalisco capital, Guadalajara, news network Milenio reported.

Angel Garcia, a 50-year-old Mexico City protester, said the demonstrations were also an appeal to the Supreme Court to rule the INE overhaul violated the Constitution.

If Mexico did not protect the INE, its democracy would be sent "back to the past," argued Garcia, a lawyer.

"It's now or never," he said.

Lopez Obrador, a leftist who contends he was robbed of the presidency twice before he finally romped to a crushing victory in the 2018 election, argues the INE is too expensive and biased in favour of his opponents. The institute denies this.

The president has cast Sunday's protests as a partisan attempt by the opposition to discredit his government.

According to the INE, the president's overhaul violates the Constitution, curbs its independence and eliminates thousands of jobs dedicated to safeguarding the electoral process, making it harder to hold free and fair elections.

Lopez Obrador, whose approval ratings still run at 60 percent or higher in opinion polls, has also weakened other autonomous bodies that check his power on the grounds they are a drain on the public purse and hostile to his political project.

He says his INE shake-up will save US$150 million a year.

Polls show the president's National Regeneration Movement (Morena), which in just a few years has become the dominant force in Mexico, is a strong favourite to win the 2024 election.

Antonio Mondragon, a retired dentist at the Mexico City protest who voted for Lopez Obrador in 2018, said people were fed up with the president behaving like a "dictator."

"We need to get back to being a democracy," said the 83-year-old Mondragon, "because the man is going mad."

- Reuters